TrianglesTriangles GraphsGraphs Polar Form FunctionsFunctions LeftoversLeftovers Review for the Final The 104 Challenge Review for the Final Final Round

Triangles

CheckWork In any right triangle, the sum of the squares of the sides is equal to the square of the hypotenuse. Go Home Go Home 5 Point Question What is the Pythagorean Theorem?

In the triangle ABC, C = 90 o, A = 25 o and a = 3. Find b. 10 Point Question CheckWork Go Home Go Home b = 6.433

Point Question Find c in the triangle below: CheckWork Go Home Go Home 12 cm c 38 o 102 o

cm 50 Point Question Find the length of the missing side in the triangle below. CheckWork Go Home Go Home 68 o 13 cm 10 cm

Find all three missing angles in the triangle below. 100 Point Question CheckWork Go Home Go Home A = o B = o C = o A B C

Graphs

CheckWork It has an even degree and negative leading coefficient. Go Home Go Home The graph of a polynomial falls to both the left and right. What can we tell about the polynomial? 5 Point Question

10 Point Question Sketch the graph of y = 3cos(2x) – 5. CheckWork Go Home Go Home period is Pi, amplitude is 3, midline is -5. It starts at (0,-2).

25 Point Question CheckWork Go Home Go Home Find the equation for a sine function that matches the graph below. Y = 2sin(x-π/4) +4 (π/4, 4) (9π/4,4)

Find the equation for the polynomial function graphed below. 50 Point Question CheckWork Go Home Go Home Y = -2(x-3)(x+1) 2 (0,6)

Find the equation for the rational function graphed below. 100 Point Question CheckWork Go Home Go Home Y = -2(x 2 -9)/(x 2 -x-2) (0,-9)

Polar Form

Plot the polar point (3, ). 5 Point Question CheckWork Go Home Go Home 30 o 3

Convert the point (-8,-6) to polar coordinates. 10 Point Question CheckWork Go Home Go Home (10, )

-67.29i j A plane flies N 15 0 W at a speed of 260 miles per hour. Write the plane’s velocity vector in component form. 25 Point Question CheckWork Go Home Go Home

50 Point Question Write the complex number 5 – 3i in polar form. CheckWork Go Home Go Home

Compute (1 – i) 1/3. Write your answer in polar form. 2 1/6 e -πi/ Point Question CheckWork Go Home Go Home

Functions

A power function 5 Point Question What type of function is this? F(x) = 3x -2 CheckWork Go Home Go Home

Find the equation for the power function that passes through (1, 5) and (5, 1/25) 10 Point Question F(x) = 5x -3 CheckWork Go Home Go Home

Graph the polynomial f(x) = 3(x - 3) 3 (x + 20), labeling all zeros, y-intercepts and asymptotes. 25 Point Question CheckWork Go Home Go Home (3,0), (-20,0), (0,-1620)

50 Point Question Asymptotes y = 0, x=2, and x=-5, (which doesn’t show well) Intercept Points: (-4,0),(0,1/5) Intercept Points: (-4,0),(0,1/5) Sketch the graph of CheckWork Go Home Go Home (-4,0)

100 Point Question Find the exact value of cos -1 (cos(28π/25)). 22π/25 CheckWork Go Home Go Home

Leftovers

U = 3i – 5 j, V = 4i – 2j. Find the dot product of the vectors U and V. 5 Point Question CheckWork Go Home Go Home22

What is the equation for a rose curve with 8 petals of length Point Question R=3cos(4Θ) CheckWork Go Home Go Home

25 Point Question Solve the equation: tan(2Θ) = √3. Θ = π/6 + πk/2 CheckWork Go Home Go Home

50 Point Question Solve the equation: sin(x) + 2cos 2 (x) = 2 CheckWork Go Home Go Home x = πk, π/6 + 2πk, 5π/6 + 2πk

Verify the identity: 100 Point Question CheckWork Go Home Go Home sure enough…

Cable on right: 222 lbs. Cable on left: lbs Cable on left: lbs A 235 lb weight is suspended by two cables as shown in the diagram. Find the force in each cable. Final Question CheckWork Go Home Go Home 235 lbs 54 o 23 o